Permutation & Combination
Free Permutation & Combination for math. Enter values to solve step-by-step with verified formulas, worked examples, and detailed explanations.
Formula
nPr = n!/(n-r)! | nCr = n!/(r!(n-r)!)
nPr calculates arrangements where order matters. nCr calculates selections where order doesn't matter.
Worked Examples
Example 1: Race Winners
Problem:8 runners, top 3 places
Solution:Order matters (Gold, Silver, Bronze). 8P3 = 8!/5! = 8×7×6 = 336.
Result:336 ways
Example 2: Card Hand
Problem:52 cards, deal 5
Solution:Order doesn\'t matter. 52C5 = 2,598,960.
Result:2,598,960 hands
Frequently Asked Questions
What is the difference between Permutation and Combination?
Order matters in Permutations (arrangements like a lock code). Order does NOT matter in Combinations (groups like a fruit salad).
What is a Circular Permutation?
Arranging items in a circle. Since there is no "start," the formula is (n-1)!. Permutation & Combination finds linear permutations.